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New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution. (English) Zbl 1221.34245

Summary: We establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation

(p(t)([y(t)+r(t)y(τ(t))] Δ ) γ ) Δ +f(t,y(θ(t)))=0,t[t 0 ,) 𝕋

on a time scale 𝕋, where |f(t,u)|q(t)|u γ |, r,p and q are real valued rd-continuous positive functions defined on 𝕋, γ1 is the quotient of odd positive integers. Our results improve previous existence results in the sense that our results do not require p Δ (t)0, and t 0 θ γ (s)q(s)[1-r(θ(s))] γ Δs=. Some examples are given to illustrate the main results.

MSC:
34N05Dynamic equations on time scales or measure chains
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
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